This invention relates to synchronous data transmission systems and more particularly to a method and an apparatus for determining the initial values of the coefficients of a transversal equalizer.
In data transmission systems, the sequence of bits, or message, to be transmitted is first coverted into a sequence of symbols. Each of them may assume a discrete number of values generally equal to a power of two. Then, these symbols are transmitted through a transmission channel at a given rate in the form of pulses which may or may not be modulated depending on whether or not the transmission system uses a carrier modulation technique. In general, the transmission channels and more particularly the telephone lines, introduce phase and amplitude distortions which modify the shape of the transmitted signals. These distortions are generally due to imperfect characteristics of the transmission channels and are increased by noise introduced into the transmission channel by certain external sources which are more or less difficult to control. In general, amplitude and phase distortions cause an interaction between the successively emitted signals. This interaction is known as intersymbol interference and precludes reliable detection of the transmitted data by the receiver. In high speed data transmission systems, the receiver is generally provided with a device for minimizing the effects of the intersymbol interference before the data are detected. Such a device is known as an equalizer.
The most widely used type of equalizer is the automatic transversal equalizer described, for example, in Chapter 6 of the book, "Principles of Data Communication," by R. W. Lucky, J. Salz and E. J. Weldon, Jr., published by the McGraw-Hill Book Company, New York, in 1968. A typical automatic transversal equalizer consists of a transversal filter, the coefficients of which are automatically adjusted so as to satisfy a given performance criterion. In general, during a first so-called "training period," a series of isolated test pulses or pseudo-random training sequence is transmitted to allow the adjustment of the equalizer coefficients to initial values as close as possible to optimum values. At the end of the training period, the initial values of the coefficients are fixed during the transmission of the message if the equalizer is not adaptive or the coefficients can be continuously adjusted during the transmission of the message if the equalizer is adaptive.
The article, "Automatic Equalization for Digital Communication," by R. W. Lucky, published in the Bell System Technical Journal of April, 1965, pages 547-588, shows the use of isolated test pulses for determining the initial values of the coefficients of an automatic transversal equalizer. In the device described in this article, after reception of each test pulse, the coefficients are adjusted so as to force to zero the shape of the impulse response at sampling instants other than a predetermined sampling instant chosen as a reference. This technique is slow and requires a great deal of power in the emitted signal when the channel is very noisy.
The article, "An Automatic Equalizer for General Purpose Communication Channels," by R. W. Lucky and H. R. Rudin published in the same journal of November, 1967, pages 2179-2208, describes the use of pseudo-random binary sequences for determining the initial values of the coefficients of an automatic transversal equalizer. In the described device, the coefficients are adjusted so as to minimize the mean square error between the equalizer output signals and a locally generated sequence identical to the one transmitted by the emitter. This technique is also slow since it requires the preliminary synchronization of the local sequence with respect to the emitted sequence and does not, in general, provide optimum initial values of the coefficients.
When the distortion characteristics of the transmission channel vary between successive messages, which is generally the case when telephone lines are used as a transmission channel, it is necessary to provide a training period prior to the transmission of each message. The efficiency of a data transmission system is generally defined as the ratio existing between the time required to transmit a message and the time the line is occupied, the latter period mainly corresponding to the training period of the equalizer to which must be added the duration of the message. To maintain this efficiency at an appropriate level in high speed transmission systems, which systems transmit a message in a few tenths of a millisecond, it is imperative to provide a method and apparatus which reduces as much as possible the training period, i.e., to determine, as quickly as possible, the initial values of the equalizer coefficients.
As indicated above, both described techniques for determining the initial values of the transversal equalizer coefficients are slow.
The article, "Cyclic Equalization -- A New Rapidly Converging Equalization Technique for Synchronous Data Communication," by K. H. Mueller and D. A. Spaulding, published in the Bell System Technical Journal of February, 1975, pages 369-406, describes a technique permitting rapid determination of the initial values of the transversal equalizer coefficients. According to this technique, the use of a periodic binary pseudo-random sequence whose period is equal to that of the equalizer, avoids the preliminary synchronization of the local sequence with the emitted sequence. The coefficients are conventionally adjusted to minimize the mean square error between the equalizer output signals and the local sequence without synchronizing the latter with the emitted sequence. At the end of the training period, the coefficients are cyclically shifted to associate the highest coefficient to a reference tap of the equalizer. However, this technique which has greatly improved the fast determination of the initial values of transversal equalizer coefficients, exhibits disadvantages when it is used with binary pseudo-random sequences as described in the article. In effect, the use of these sequences does not theoretically provide the optimum values of the equalizer coefficients nor does it provide them as quickly as possible.
An object of this invention is to overcome these disadvantages by providing a method and an apparatus for determining the optimum theoretical values of transversal equalizer coefficients.
Another object of this invention is to provide a method and an apparatus providing a very fast determination of the optimum theoretical values of transversal equalizer coefficients.
Another object of this invention is to provide a method and an apparatus which yields a very fast determination of the optimum theoretical values of transversal equalizer coefficients by using a direct method.
In general, this invention provides a process for determining the initial values of the coefficients of a transversal equalizer, including the following steps.
1. selecting a sequence (u.sub.i) of L binary elements u.sub.i among the periodic binary pseudo-random sequences of length L, such that: EQU A.sub.0 = L and A.sub.j = -1 j = 1,2, . . . , (i L-1)
where ##EQU1##
2. adding to each element u.sub.i of the sequence (u.sub.i), a corrective term m determined by the following relation: ##EQU2## whereby building a sequence (v.sub.i) of L elements v.sub.i where v.sub.i =u.sub.i + m;
3. transmitting the sequence (v.sub.i) obtained in this way, and
4. determining the values of the equalizer coefficients from the received sequence.
According to a preferred embodiment of the invention, the values of the equalizer coefficients are determined by performing the following steps:
1. determining samples r.sub.j of the impulse response of the transmission channel by using the following cross-correlation relation: ##EQU3## in which the x.sub.i 's represent the elements of the received sequence,
2. calculating autocorrelation matrix B of the samples of the transmission channel impulse response and
3. determining the values of the equalizer coefficients by using the following matrix relation: EQU C.sub.opt = B.sup.-1 R
in which:
C.sub.opt is the column matrix of the coefficient set, PA1 B.sup.-1 is inversed matrix B and PA1 R is the inversed column vector of the samples of the transmission channel impulse reponse.